Complex hyperbolic free groups with many parabolic elements

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in ${\rm PU}(2,1)$ such that the boundary loops are mapped to ${\rm PU}(2,1)$. We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of $(3,3,\infty)$-groups. In particular we prove that it is possible to construct representations of the free group of rank two \la a,b\ra in ${\rm PU}(2,1)$ for which $a$, $b$, $ab$, $ab^{-1}$, $ab^2$, $a^2b$ and $[a,b]$ all are mapped to parabolics.Comment: 21 pages, 11 figure

Making Windows into Men’s Souls: An Examination of Theological Norms at Elizabethan Cambridge

The nature of English religiosity that is both specific ideology and doctrine and how these were practiced in the adherent\u27s day to day life, during the later part of the Tudor dynasty has been the subject of much debate and research. Due to the volume of work produced about this period it is necessary to differentiate between three categories: those works which are directly relevant to this examination, as they deal specifically with either the time or content of this essay, those which are useful to understanding the period directly preceding this examinations focus, and those which address subjects and themes which are largely outside the scope of this paper. By necessity this means that this paper will not exam or address a large segment of the work produced surrounding Elizabethan religiosity, This should not be taken to mean that those works which the author does not examine are without merit or validity, merely that this field is one in which a large and diverse body of work has been produced. There were also several phases to the Reformation in England and what holds true in one does not necessarily hold in the other. This essay is intended only to address those norms present at Cambridge during the reign of Elizabeth Tudor

Traces in complex hyperbolic geometry.

We discuss the relationship between the geometry of complex hyperbolic manifolds and orbifolds and the traces of elements of the corresponding subgroup of SU(2, 1). We begin by showing how geometrical information about individual isometries is encoded by their trace. We then consider traces for groups Γ of isometries in two specific cases. First, we consider the case where Γ is a free group on two generators, which we view as the fundamental group of a three holed sphere. We indicate how to use this analysis to give complex hyperbolic Fenchel-Nielsen coordinates. Secondly, we consider the case where Γ is a triangle group generated by complex reflections in three complex lines. We keep in mind similar results from the more familiar setting of Fuchsian and Kleinian groups and we explain those examples from our point of view

Trophic Transfer of Arsenic from an Aquatic Insect to Terrestrial Insect Predators.

The movement of energy and nutrients from aquatic to terrestrial ecosystems can be substantial, and emergent aquatic insects can serve as biovectors not only for nutrients, but also for contaminants present in the aquatic environment. The terrestrial predators Tenodera aridifolia sinensis (Mantodea: Mantidae) and Tidarren haemorrhoidale (Araneae: Theridiidae) and the aquatic predator Buenoa scimitra (Hemiptera: Notonectidae) were chosen to evaluate the efficacy of arsenic transfer between aquatic and terrestrial environments. Culex tarsalis larvae were reared in either control water or water containing 1000 µg l(-1) arsenic. Adults that emerged from the control and arsenic treatments were fed to the terrestrial predators, and fourth instar larvae were fed to the aquatic predator reared in control or arsenic contaminated water. Tenodera a. sinensis fed arsenic-treated Cx. tarsalis accumulated 658±130 ng g(-1) of arsenic. There was no significant difference between control and arsenic-fed T. haemorrhoidale (range 142-290 ng g(-1)). Buenoa scimitra accumulated 5120±406 ng g(-1) of arsenic when exposed to arsenic-fed Cx. tarsalis and reared in water containing 1000 µg l(-1) arsenic. There was no significant difference between controls or arsenic-fed B. scimitra that were not exposed to water-borne arsenic, indicating that for this species environmental exposure was more important in accumulation than strictly dietary arsenic. These results indicate that transfer to terrestrial predators may play an important role in arsenic cycling, which would be particularly true during periods of mass emergence of potential insect biovectors. Trophic transfer within the aquatic environment may still occur with secondary predation, or in predators with different feeding strategies

Constraint Identification In On-Demand Mobility For Aviation Through An Exploratory Case Study Of Los Angeles

On-Demand Mobility (ODM) for Aviation is an emerging concept that proposes to provide aircraft-based, point-to-point transportation to consumers within a metropolitan area. This paper explicitly identified key operational constraints facing ODM Aviation networks and assessed how new vehicles and technologies could mitigate or reduce the severity of these constraints. An exploratory case study was developed to evaluate hypothetical ODM Aviation services in Los Angeles and the greater Southern California region. Promising early adopter markets were identified based upon current commuting and wealth patterns. A concept of operations (ConOps) was proposed for twelve reference missions that serviced a representative subset of these markets. Review of the reference missions provided a holistic impression of the potential implementation challenges facing an ODM Aviation network in a United States metropolitan region. Five key operational constraints were identified that may inhibit the near or far-term implementation of ODM Aviation operations. The constraints identified include: aircraft noise and community acceptance, the availability of ground infrastructure, aircraft interaction with air traffic control, community access to takeoff and landing areas, and the flight density achievable in uncontrolled airspace. Furthermore, three issues were identified including electric aircraft operating standards and certifications, all-weather operational capabilities, and ODM aircraft interaction with unmanned aircraft systems

Evaluation Of Key Operational Constraints Affecting On-Demand Mobility For Aviation In The Los Angeles Basin: Ground Infrastructure, Air Traffic Control And Noise

This paper investigated three key operational constraints anticipated to impact On-Demand Mobility for Aviation markets in the Los Angeles basin including: community acceptance issues resulting from aircraft noise, the availability of takeoff and landing areas, and the scalability of operations under Air Traffic Control. The analysis provided insight into the nature of each of these constraints and potential approaches to their mitigation. First, existing ground infrastructure in Los Angeles that may support ODM Aviation operations was identified. A variety of proposed techniques to increase the geographic distribution and throughput capacity of ODM Aviation infrastructure were also evaluated. Second, ASDE-X radar tracking data from the Los Angeles International Airport was reviewed to identify areas where it may be feasible to route future ODM operations due to the low volume of conventional operations. Potential opportunities and risks associated with supplementing air traffic control through novel low-altitude management concepts such as NASA's Unmanned Aircraft System Traffic Management (UTM) program were also investigated. Finally, the influence of aircraft noise on local communities’ acceptance of aircraft operations was discussed. Various pathways through which communities may limit or prohibit aircraft operations were reviewed